Network Coding for the Internet

1. Network Coding for the Internet Philip A. Chou*, Yunnan Wu†, and Kamal Jain**Microsoft Research & †Princeton University Communication Theory Workshop, May 6-8, 2004and EPFL, May 10, 2004

2. Outline • Introduction to Network Coding • Practical Network Coding • Packetization • Buffering • Internet Applications • Live Broadcasting, File Downloading, Messaging, Interactive Communication

3. Network Coding Introduction • Directed graph with edge capacities • Sender s, set of receivers T • Ask: Maximum rate to broadcast info from s to T ? sender s receiver t in T

4. Maximum Flow • Menger (1927) – single receiver • Maxflow(s,t) ≤ Mincut(s,t) ≡ht achievable • Edmonds (1972) – all nodes are receivers • Maxflow(s,T) ≤ mintht≡h achievable if T=V sender s receiver t in T

5. Network Coding Maximizes Throughput a • Alswede, Cai, Li, Yeung (2000) • NC always achieves h = mintht • Li, Yeung, Cai (2003) • Koetter and Médard (2003) a,b a a a+b a+b a,b a+b b b b a,b optimal multicastthroughput = 1 network codingthroughput = 2 sender receiver coding node

6. b b a b a b a+b a b a a+b a Network Coding Minimizes Delay • Jain and Chou (2004) • Reconstruction delay at any node t is no greater thanthe maximum path length in any flow from s to t. optimal multicastdelay = 3 network codingdelay = 2

7. a+b a+b b a a a a a b a a a a a b b Network Coding Minimizes Energy (per bit) a a,b • Wu et al. (2003); Wu, Chou, Kung (2004) • Lun, Médard, Ho, Koetter (2004) a a a,b a b b,a optimal multicastenergy per bit = 5 network codingenergy per bit = 4.5

8. Network Coding Applicable to Real Networks? • Internet • IP Layer • Routers (e.g., ISP) • Application Layer • Infrastructure (e.g., CDN) • Ad hoc (e.g., P2P) • Wireless • Mobile ad hoc multihop wireless networks • Sensor networks • Stationary wireless (residential) mesh networks

9. Theory vs. Practice (1/4) • Theory: • Symbols flow synchronously throughout network; edges have integral capacities • Practice: • Information travels asynchronously in packets; packets subject to random delays and losses; edge capacitiesoften unknown, varying as competing communication processes begin/end

10. Theory vs. Practice (2/4) • Theory: • Some centralized knowledge of topology to compute capacity or coding functions • Practice: • May be difficult to obtain centralized knowledge, or to arrange its reliable broadcast to nodes across the very communication network being established

11. Theory vs. Practice (3/4) • Theory: • Can design encoding to withstand failures, but decoders must know failure pattern • Practice: • Difficult to communicate failure pattern reliably to receivers

12. Theory vs. Practice (4/4) • Theory: • Cyclic graphs present difficulties, e.g., capacity only in limit of large blocklength • Practice: • Cycles abound. If A →B then B→A.

13. Our work addresses practical network coding in real networks • Packets subject to random loss and delay • Edges have variable capacities due to congestion and other cross traffic • Node & link failures, additions, & deletions are common (as in P2P, Ad hoc networks) • Cycles are everywhere • Broadcast capacity may be unknown • No centralized knowledge of graph topology or encoder/decoder functions • Simple technology, applicable in practice

14. Approach • Packet Format • Removes need for centralized knowledge of graph topology and encoding/decoding functions • Buffer Model • Allows asynchronous packets arrivals & departures with arbitrarily varying rates, delay, loss

15. Standard Framework • Graph (V,E) having unit capacity edges • Sender s in V, set of receivers T={t,…} in V • Broadcast capacity h = mintMaxflow(s,t) • y(e) = ∑e’ me(e’) y(e’) • m(e) = [me(e’)]e’ is local encoding vector

16. Global Encoding Vectors • By induction y(e) = ∑hi=1gi(e) xi • g(e) = [g1(e),…,gh(e)] is global encoding vector • Receiver t can recover x1,…,xh from

17. Invertibility of Gt • Gt will be invertible with high probabilityif local encoding vectors are randomand field size is sufficiently large • If field size = 216 and |E| = 28then Gt will be invertible w.p. ≥ 1−2−8 = 0.996 [Ho et al., 2003] [Jaggi, Sanders, et al., 2003]

18. Packetization • Internet: MTU size typically ≈ 1400+ bytes • y(e) = ∑e’ me(e’) y(e’) = ∑hi=1gi(e) xi s.t.

19. Key Idea • Include within each packet on edge eg(e) = ∑e’ me(e’) g(e’); y(e) = ∑e’ me(e’) y(e’) • Can be accomplished by prefixing i th unit vector to i th source vector xi, i=1,…,h • Then global encoding vectors needed to invert the code at any receiver can be found in the received packets themselves!

20. Cost vs. Benefit • Cost: • Overhead of transmitting h extra symbolsper packet; if h = 50 and field size = 28,then overhead ≈50/1400 ≈ 3% • Benefit: • Receivers can decode even if • Network topology & encoding functions unknown • Nodes & edges added & removed in ad hoc way • Packet loss, node & link failures w/ unknown locations • Local encoding vectors are time-varying & random

21. Erasure Protection • Removals, failures, losses, poor random encoding may reduce capacity below h • Basic form of erasure protection:send redundant packets, e.g.,last h-k packets of x1,…, xh are known zero

22. Priority Encoding Transmission (Albanese et al., IEEE Trans IT ’96) • More sophisticated form: partition data into layers of importance, vary redundancy by layer • Received rank k→ recover k layers • Exact capacity can be unknown

23. Asynchronous Communication • In real networks, “unit capacity” edges grouped • Packets on real edges carried sequentially • Separate edges → separate prop & queuing delays • Number of packets per unit time on edge varies • Loss, congestion, competing traffic, rounding • Need to synchronize • All packets related to same source vectors x1,…, xh are in same generation; h is generation size • All packets in same generation tagged with same generation number; one byte (mod 256) sufficient

24. Buffering edge Transmission opportunity: generate packet random combination arriving packets (jitter, loss, variable rate) edge edge buffer asynchronous reception asynchronous transmission edge node

25. Decoding • Block decoding: • Collect h or more packets, hope to invert Gt • Earliest decoding (recommended): • Perform Gaussian elimination after each packet • At every node, detect & discard non-informative packets • Gt tends to be lower triangular, so can typically decode x1,…,xk with fewer more than k packets • Much lower decoding delay than block decoding • Approximately constant, independent of block length h

26. Flushing Policy, Delay Spread,and Throughput loss • Policy: flush when first packet of next generation arrives on any edge • Simple, robust, but leads to some throughput loss

27. Interleaving • Decomposes session into several concurrent interleaved sessions with lower sending rates • Does not decrease overall sending rate • Increases space between packets in each session; decreases relative delay spread

28. Simulations • Implemented event-driven simulator in C++ • Six ISP graphs from Rocketfuel project (UW) • SprintLink: 89 nodes, 972 bidirectional edges • Edge capacities: scaled to 1 Gbps / “cost” • Edge latencies: speed of light x distance • Sender: Seattle; Receivers: 20 arbitrary (5 shown) • Broadcast capacity: 450 Mbps; Max 833 Mbps • Union of maxflows: 89 nodes, 207 edges • Send 20000 packets in each experiment, measure: • received rank, throughput, throughput loss, decoding delay vs.sendingRate(450), fieldSize(216), genSize(100), intLen(100)

30. Received Rank

31. Throughput

32. Throughput Loss

33. Decoding Delay

34. Network Coding for Internet and Wireless Applications File download wireless Interactive Communication (conferencing, gaming) Live broadcast Media on demand Download from peer Coded download Parallel download Instant Messaging Internet Infra-structure (CDN) AkamaiRBN Ad Hoc (P2P) ALM SplitStreamCoopNet Gnutella Kazaa Digital Fountain BitTorrent PeerNet Windows Messenger XboxLive

35. Live Broadcast (1/2) • State-of-the-art: Application Layer Multicast (ALM) trees with disjoint edges (e.g., CoopNet) • FEC/MDC striped across trees • Up/download bandwidths equalized a failed node

36. Live Broadcast (2/2) • Network Coding [Jain, Lovász, Chou (2004)]: • Does not propagate losses/failures beyond child • ALM/CoopNet average throughput: (1–ε)depth * sending rateNetwork Coding average throughput: (1–ε) * sending rate failed node affected nodes(maxflow: ht→ ht – 1) unaffected nodes(maxflow unchanged)

37. File Download • State-of-the-Art: Parallel download (e.g., BitTorrent) • Selects parents at random • Reconciles working sets • Flash crowds stressful • Network Coding: • Does not need to reconcile working sets • Handles flash crowds similarly to live broadcast • Throughput download time • Seamlessly transitions from broadcast to download mode

38. Instant Messaging • State-of-the-Art: Flooding (e.g., PeerNet) • Peer Name Resolution Protocol (distributed hash table) • Maintains group as graph with 3-7 neighbors per node • Messaging service: push down at source, pops up at receivers • How? Flooding • Adaptive, reliable • 3-7x over-use • Network Coding: • Improves network usage 3-7x (since all packets informative) • Scales naturally from short message to long flows

39. Interactive Communication in mobile ad hoc wireless networks • State-of-the-Art: Route discovery and maintenance • Timeliness, reliability • Network Coding: • Is as distributed, robust, and adaptive as flooding • Each node becomes collector and beacon of information • Minimizes delay without having to find minimum delay route

40. a b a+b a+b Physical Piggybacking • Information sent from t to s can be piggybacked on information sent from s to t • Network coding helps even with point-to-point interactive communication • throughput • energy per bit • delay s t

41. Summary • Network Coding is Practical • Packetization • Buffering • Network Coding can improve performance • in IP or wireless networks • in infrastructure-based or P2P networks • for live broadcast, file download, messaging, interactive communication • by improving throughput, robustness, delay, manageability, energy consumption • even if all nodes are receivers, even for point-to-point communication